Quant Strat Superday Probability + Fixed Income Drill

Quant Strat Superday rounds combine probability brainteasers, short coding around stochastic processes, and fixed-income domain knowledge. The interview is verbal-heavy and rewards clear variable definitions and assumptions. Requirements Representative probability / coding prompts: Fair 12-sided die: expected number of rolls needed to see all faces. One 10-sided die and one 6-sided die: choose a guessed sum; if correct, profit equals that sum. Find expected gain / optimal choice. Given 101 numbers, decide whether at least one subset sum must be divisible by 11. Fair 6-sided die with profit equal to the roll; you may re-roll up to three rounds. Find expected gain. Same re-roll game, but each toss costs 1. Find expected gain. Implement the re-roll expected-gain calculation in Python. Sample from or code a probability process such as a biased random walk on a manifold. Representative fixed-income / domain prompts: Rank credit card, car loan, mortgage, and bond interest rates from high to low and explain why. Explain when a borrower prepays and how prepayment relates to interest rates. Define duration. Explain how expiration, coupon size, and coupon frequency affect duration. State the direction of the relationship between fixed-income price and interest rate. Notes Julia is acceptable in at least some quant-track screens, but Python is still the safest default unless the interviewer invites another language. The campus Superday format is often two 45-minute rounds with one or two interviewers per round; each round can mix behavioral, coding, and probability. Preparation Work through stopping-time and coupon-collector expectations until you can narrate the recurrence aloud. Code small expected-value recurrences in Python, including finite-horizon re-roll decisions. Review duration, prepayment, and basic credit-product rate ordering at a conceptual level.